The bill amount for Diana's brunch was $35.80. She wanted to leave 18% of the total bill as a tip. How much should the tip
be?

Answer:

A. yes the y-intercept is 2

B. the graph is a straight line

C. The Slope of the Line is 1/2

D. The line Does Not pass through the origin

Step-by-step explanation:

A. the y-intercept is when x=0... y=([tex]\frac{-1}{2}[/tex]*0)+2

B. It is a straight line because x is raised to the 1st power and not another number

C. Although the slope of the equation is [tex]\frac{-1}{2}[/tex]... the slope is still 1/2

D. The line Does Not pass through the origin

origin= (0,0)

x=0 --> y=([tex]\frac{-1}{2}[/tex]*0)+2=

y=0---> 0=([tex]\frac{-1}{2}[/tex]*x)+2

[tex]\frac{-x}{2}[/tex]=2---> x=-4

Answer:

The first two statements are true.

Click "The y-intercept of the line is 2" and "The graph is a straight line"

Step-by-step explanation:

The most important thing to know for this question is the equation of a line, y=mx+c, where m is the slope of the line and c is the y-intercept (where the lines crosses the y-axis).

Our formula is y= - [tex]\frac{1}{2}[/tex]x+2, which means the y-intercept is 2. Therefore, the first statement is true.

The equation follows the general equation for a straight line, so the second statement is true.

Our formula is y= - [tex]\frac{1}{2}[/tex]x+2, which means the slope is -  [tex]\frac{1}{2}[/tex], not  [tex]\frac{1}{2}[/tex]. Therefore, the third statement is not true.

For a line to pass through the origin (0,0), it's y-intercept must be 0, but we already know the y-intercept here is 2. Therefore, the fourth statement is not true.

To see if the line passes through (0, -2), we must sub these values into the equation and see if it makes sense

y= - [tex]\frac{1}{2}[/tex]x+2?

-2=- [tex]\frac{1}{2}[/tex](0)+2?

-2 = 2? This is not true, so the last statement is also not true.

If Shureka Washburn has scores of ​69, 74​, 79​, and 62 on her algebra tests, then by using the inequality, the score she must make on the final exam to pass the course with an average of 71 or higher is 71

The scores she scored on test = 69, 74, 79, 62

Consider the final score she must make on the final exam as x

Sum of the scores = 69+74+79+62+2x

= 284+2x

Consider the average of score = Sum of scores / Number of subjects

= (284+2x)/6

She need average of 71 or higher

Then the inequality equation will be

(284+2x)/6 ≥ 71

284+2x ≥ 426

2x ≥ 426-284

2x ≥ 142

x ≥ 71

Hence, if Shureka Washburn has scores of ​69, 74​, 79​, and 62 on her algebra tests, then by using the inequality, the score she must make on the final exam to pass the course with an average of 71 or higher is 71

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27 ft. can be used to represent the water's surface if the platform is 15 ft. above the pool surface and the pool has a depth of 12 ft.

As Sadie stands on a platform that is 15 ft. above the pool surface. The pool has a depth of 12 ft. then, and the total height of the water surface is, the total hight,

The total height = distance between pool surface to platform + the depth of the pool

∵ The total height =  15 ft. + 12 ft.= 27 ft.

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The corresponding values of the lower and upper bounds of m - n are 41.41 and 41.59.

What are the values of the lower and upper bounds of m - n?

Upper and lower bounds are the possible maximum and minimum values of a number before it was rounded.

The upper and lower bounds can be expressed using the error interval

The lowest value of m is 48.15

The highest value of m is 48.24

The lowest value of n is 6.65

The highest value of n is 6.74

Therefore, lower bound of m - n = 48.15 - 6.74 = 41.41

Also, the upper bound of m - n = 48.24 - 6.65  = 41.59

So values of the lower and upper bounds of m - n are 41.41 and 41.59 respectively.

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Answer:

2

9c and a

Step-by-step explanation:

Answer:

2, (a and c)

Step-by-step explanation:

Answer:

{-4; -5}

Step-by-step explanation:

just put any integer from set S in place of p and you will know. the inequality is false with -2 and -3, but with other two numbers is true

they seem to be right :p

Step-by-step explanation:

The y-intercept and the horizontal asymptote of g(x) = 7ˣ + 2 is (a) (0, 3) ; y = 2

The equation of the function is given as

g(x) = 7ˣ + 2

To calculate the y-intercept, we set x = 0

So, we have

g(0) = 7⁰ + 2

Evaluate the exponent

g(0) = 1 + 2

Evaluate the sum

g(0) = 3

So, we have

(x, y) = (0, 3)

The equation of the function is given as

g(x) = 7ˣ + 2

To calculate the horizontal asymptote, we set 7ˣ

So, we have

y = 0 + 2

Evaluate the sum

y = 2

Hence, the solution is (a) (0, 3) ; y = 2

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The required y-intercept of the given function is (0,3) and the horizontal asymptote is y = 2.

Asymptote is the line on the curve that does not intersect the curve but passes as near to the maximum and minimum of the graph.

Here,
The y-intercept of the given function is evaluated as put the x coordinate to zero,
So,
g(0) = 1 + 2
g(0) = 3

Now, the horizontal asymptote is a line that passes near to the line but does not intersect with the curve,
So,
Terminating the x compositon of the function 7ˣ = 0 the rest will be the horizontal asymptote,
y = 7ˣ + 2
y =  0 + 2
y = 2

Thus,  the required y-intercept of the given function is (0,3) and the horizontal asymptote is y = 2.

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Answer:

Both the lights will flash 1440 times a day. Proof: Red light flashes after every 30 seconds and green light flashes after every 20 seconds.

Step-by-step explanation:

Answer:

11) 7d + 28 and 7(d+4)

12) y^2 + 3y and y(y+3)

Step-by-step explanation:

The value of f(3) for the given expression is 8.

What is evaluation of an expression?
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Finding the value of an algebraic expression when a specified integer is used to replace a variable is known as evaluating the expression. We use the given number to replace the expression's variable before applying the order of operations to simplify the expression. The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.

Given, the expression is 5(x - 1) - 2
Let y = f(x) = 5(x - 1) - 2 = 5x - 5 - 2 = 5x - 7
Therefore, f(3) using the equation above is: f(3) = 5(3) - 7 = 8
Thus, the value of f(3) or y at x = 3 for the given expression is 8.

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Joan walked 20 brown dogs.

As per the question, the 40% of total number of dogs are brown. So, finding 40% of the number 50 will give us the number of brown dogs.

Number of brown dogs = 50×40%

Converting Percentage to fraction

Number of brown dogs = 50×40/100

Cancelling zero as it is common

Number of brown dogs = 5×4

Performing multiplication to find the number of brown dogs

Number of brown dogs = 20

Thus, out of 50 dogs, Joan walked 20 brown dogs.

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Answer:

y = 0.57143x - 4

Step-by-step explanation:

The range of the function f (x) = -3x are (0, -3, 6).

What is Domain?

The set of all inputs of the function is called Domain of set.

Given that;

The domain of f(x) = -3x is (0, 1, 2).

Now, Domain of the function are the values of x.

So, We find the Range of the function as;

Substitute all the values of domain (x) in the given function as;

The function is;

f (x) = -3x

For x = 0

Range = f (x) = - 3 × 0 = 0

For x = 1;

Range = f (x) = - 3 × 1 = -3

For x = 2

Range = f (x) = 3 × 2 = 6

Thus, Range of the function are (0, -3, 6)

Therefore, The range of the function f (x) = -3x are (0, -3, 6).

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Answer:

g + 1199 / 8

Step-by-step explanation:

3/4+65/8-23+78+92-6+g

1199/8+g

When the spacecraft launched, it was 254 miles away from the Earth and its distance away from the Earth is increasing at a rate of 270 miles per hour.

The equation that represents the distance of the space craft is known as a linear equation. A linear equation is an equation that has only one variable that is raised to the power of one.

A linear equation increases or decreases at a constant rate. When drawn on a graph, a linear equation is a straight curve that slopes either upward or downward.

A linear equation usually has this form y = mx + b

Where:

D = 254 + 270t

Where:

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use the cross multiplication method :)

An equation is a collection of variables and constants with the value of x which will make the equation 7+3(x - 1)=5x+-2(x+1) to be true is 1/2.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

As per the given equation,

7+3(x - 1)=5x+-2(x+1)

7 + 3x - 3 = 5x + 2x + 2

3x + 4 = 7x + 2

7x + 2 = 3x + 4

7x - 3x = 4 - 2

4x = 2

x = 1/2

Hence "The value of x which will make the equation 7+3(x - 1)=5x+-2(x+1) to be true is 1/2".

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Answer:

Plot the point (6, 2). From there, move 3 units up and then 4 units to the left. You will be at (2, 5). Plot that point, and then draw a line through (6, 2) and (2, 5).

Simply subtract the lowest value from the highest value in the data set to determine the range.

Find the biggest observed value of a variable (the maximum) and subtract the smallest observed value to determine the range (the minimum). The data points between the distribution's two extremes are not taken into account by the range; just these two values are.

Because of its sensitivity to extreme values, it is frequently employed as a supplement to other measures of dispersion rather than as the single measure.

To help find the quartiles for bigger data sets, you can utilise the cumulative relative frequency distribution or, even better, the fundamental statistics algorithms found in spreadsheets or statistical applications that provide results more quickly.

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The distributive property for the product of 27x34 will give a value of 918.

It should be noted that distributive property simply means that one can distribute the contents of the parentheses into the other so that one can get the answer.

The distributive property is illustrated as:

a × (b + c) = a×b + a×c

In this case, using distributive property to find the product 27x34 will be:

=27x(30+4)

= 27 × 30 + 27 × 4

= 810 + 108

= 918

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Answer:

p(x) is a function, and a polynomial of degree 3, then

By remainder theorem and factor theorem,

p(0) = p(1) = p (-1) = 0 if and only if

x = 0, 1, -1 are zeroes if and only if

p(x) = k(x - 0)(x - 1)(x + 1) = k(x)(x^2 - 1) = k(x^3 - x) = kx^3 - kx

p(2) = k(2)^3 - k(2) = 6

8k - 2k = 6

6k = 6

k = 1

Thus p(x) = x(x - 1)(x + 1) = x(x^2 - 1) = x^3 - x

p(-x) = (-x)^3 - (-x) = x^3 + x

-p(x) = -(x^3 - x) = -x^3 + x

As you can see, p(x) does not equal to -p(x), unless x = 0, 1, -1,

because p(0) = -p(0) = 0, p(-1) = - p(1) = 0, p(1) = -p(-1) = 0

p(x) = x(x - 1)(x + 1)

If x < -1, then x < 0, x - 1 < 0, x + 1 < 0

That means p(x) < 0

If -1 < x < 0, then x < 0, -2 < x - 1 < -1 < 0, 0 < x + 1 < 1

That means p(x) > 0

If 0 < x < 1, then x > 0, -1 < x - 1 < 0, 0 < 1 < x + 1 < 2

That means p(x) < 0

If x > 1, then x > 0, x - 1 > 0, x + 1 > 2 > 0

That means p(x) > 0

Thus p(x) < 0 if x < -1 or 0 < x < 1

Using the exponential distribution, there is a 0.263 probability that a truck will be loaded in 20 minutes or more.

The exponential probability distribution, with mean m, is described by the following probability mass function:

[tex]f(x) = \mu e^{-\mu x}[/tex]

[tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

The integral has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

Hence the probability of finding a value higher than x is given by:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

In the context of this problem, the mean and the decay parameter are given, respectively, by:

[tex]m = 15, \mu = \frac{1}{15} = 0.0667[/tex]

Hence the probability that a truck will be loaded in 20 minutes or more is:

[tex]P(X > 20) = e^{-0.0667 \times 20} = 0.263[/tex]

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The cups of sugar needed is 2.5 cups.

The cups of flour needed is 3.75 cups

The cups of butter needed is 1.25 cups.

Given the information in the question, the ratio of sugar to flour to butter is 1 : 1.5 : 0.5

Cups of sugar needed = (ratio representing sugar / sum of ratios) x total number of cups

Sum of ratios = 1 + 1.5 + 0.5 = 3

Cups of sugar needed = (1 / 3) x 7.5 = 2.5 cups

Cups of flour needed = (ratio representing flour / sum of ratios) x total number of cups

Cups of flour needed = (1.5 / 3) x 7.5 = 3.75 cups

Cups of butter needed = (ratio representing butter / sum of ratios) x total number of cups

Cups of butter needed = (0.5 / 3) x 7.5 = 1.25 cups

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STEP 1

Interpret question to make sense geometrically.

We have circular shapes, thus, we are dealing with circles and these circles have their area, however, we seek the angle with which when used to cut the circle will give us an area of 220 sq cm.

Note that this is a fraction of the total area of the circle.

This will be illustrated diagrammatically below

Area of a sector is given as:

STEP 2

Find unknown

The ci

(i) cosФ = 4/7 and sinФ is negative → It lies in the 4th quadrant 304.8° and the suitable graph is not provided here.

(ii) secФ = -13/5 and tanФ is negative  → It lies in the IInd quadrant 112.6° and the suitable graph is J.

(iii) sinФ = 7/10 and cotФ is positive  → It lies in Ist quadrant =44.4° and the suitable graph is I.

(iv) tan0 = 3/4 and sin0 is negative  → It lies in the IIIrd quadrant 216.9° and the suitable graph is not provided here.

What is quadrant?

(i) cosФ = 4/7 and sinФ is negative

Ф=cos^(-1)(4/7)= 55.2°

It lies in 4th quadrant (360-55.2)°=304.8°

A suitable graph is not provided here.

(ii) secФ = -13/5 and tanФ is negative.

Ф=sec^(-1)(-13/5)=67.4°

It lies in IInd quadrant (180-67.4°)=112.6°

A suitable graph is J.

(iii) sinФ = 7/10 and cotФ is positive.

Ф=sin^(-1)(7/10)=44.4°

It lies in Ist quadrant =44.4°

A suitable graph is I.

(iv) tan0 = 3/4 and sin0 is negative.

Ф=tan^(-1)(3/4)=36.9°

It lies in IIIrd quadrant (180+36.9)=216.9°

A suitable graph is not provided here.

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The product of 3.7x x 6x = (3.7 x 6) x (x x x) = 22.2x².

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It is not possible to create a complex number in which b = 0, as it would be equivalent to a real number.

The general format of a complex number is given as follows:

z = a + bi.

The meaning of the parameters a and b are given as follows:

If the coefficient b has a value of zero, then the complex number is written as follows:

z = a + 0i.

z = a.

Which is equivalent to a real number, that is, the number would have only a real component, hence it is not possible to find an imaginary number with b = 0.

Basically, any real number can be represented as a complex number with imaginary part 0, but then the number would not be complex.

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